CA Package

8/10/2019 CA Package

1/22

Package ca

December 22, 2014

Version 0.55

Date 2014-03-09

Title Simple, Multiple and Joint Correspondence Analysis

Maintainer Oleg Nenadic

Depends R (>= 2.8.0)

Suggests rgl (>= 0.64-10)

Description A package for computation and visualization of simple, multiple and joint correspon-

dence analysis.

LazyLoad yes

LazyData yes

License GPL

URL http://www.carme-n.org/

Author Michael Greenacre [aut],

Oleg Nenadic [aut, cre],Michael Friendly [ctb]

Repository CRAN

Repository/R-Forge/Project ca0

Repository/R-Forge/Revision 6

Repository/R-Forge/DateTimeStamp 2014-03-11 14:21:56

Date/Publication 2014-07-06 17:44:54

NeedsCompilation no

R topics documented:

author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

iterate.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

pchlist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

plot.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1
http://www.carme-n.org/http://www.carme-n.org/


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2 ca

plot.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

plot3d.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

print.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

print.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

print.summary.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

print.summary.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

smoke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

summary.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

summary.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

wg93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Index 22

author Author dataset

Description

This data matrix contains the counts of the 26 letters of the alphabet (columns of matrix) for 12

different novels (rows of matrix). Each row contains letter counts in a sample of text from each

work, excluding proper nouns.

Usage

data("author")

Format

Data frame containing the 12 x 26 matrix.

Source

Larsen, W.A. and McGill, R., unpublished data collected in 1973.

ca Simple correspondence analysis

Description

Computation of simple correspondence analysis.


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ca 3

Usage

ca(obj, ...)

## S3 method for class matrix

ca(obj, nd = NA, suprow = NA, supcol = NA,

subsetrow = NA, subsetcol = NA, ...)

## S3 method for class data.frame

ca(obj, ...)

## S3 method for class table

ca(obj, ...)

## S3 method for class xtabs

ca(obj, ...)

## S3 method for class formula

ca(formula, data, ...)

Arguments

obj,formula The function is generic, accepting various forms of the principal argument for

specifying a two-way frequency table. Currently accepted forms are matrices,

data frames (coerced to frequency tables), objects of class "xtabs"or "table"

and one-sided formulae of the form~ F1 + F2, whereF1and F2are factors.

nd Number of dimensions to be included in the output; if NA the maximum possible

dimensions are included.

suprow Indices of supplementary rows.

supcol Indices of supplementary columns.

subsetrow Row indices of subset.

subsetcol Column indices of subset.

data A data frame against which to preferentially resolve variables in theformula

... Other arguments passed to the ca.matrix method

Details

The functionca computes a simple correspondence analysis based on the singular value decompo-

sition.

The options suprowand supcolallow supplementary (passive) rows and columns to be specified.

Using the options subsetrowand/orsubsetcolresult in a subset CA being performed.

Value

sv Singular values

nd Dimenson of the solution


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4 ca

rownames Row names

rowmass Row masses

rowdist Row chi-square distances to centroid

rowinertia Row inertias

rowcoord Row standard coordinates

rowsup Indices of row supplementary points

colnames Column names

colmass Column masses

coldist Column chi-square distances to centroid

colinertia Column inertias

colcoord Column standard coordinates

colsup Indices of column supplementary points

References

Nenadic, O. and Greenacre, M. (2007). Correspondence analysis in R, with two- and three-dimensional

graphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/

v20/i03/

Greenacre, M. (2007). Correspondence Analysis in Practice. Second Edition. London: Chapman

& Hall / CRC.

Blasius, J. and Greenacre, M. J. (1994), Computation of correspondence analysis, in Correspon-

dence Analysis in the Social Sciences, pp. 53-75, London: Academic Press.

Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationships

among a selected set of response categories from a questionnaire survey. Sociological Methods and

Research,35, pp. 193-218.

See Also

svd,plot.ca,plot3d.ca,summary.ca,print.ca

Examples

data("author")

ca(author)

plot(ca(author))

# table method

haireye


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iterate.mjca 5

iterate.mjca Updating a Burt matrix in Joint Correspondence Analysis

Description

Updating a Burt matrix in Joint Correspondence Analysis based on iteratively weighted least squares.

Usage

iterate.mjca(B, lev.n, nd = 2, maxit = 50, epsilon = 0.0001)

Arguments

B A Burt matrix.

lev.n The number of levels for each factor from the original response pattern matrix.

nd The required dimensionality of the solution.

maxit The maximum number of iterations.

epsilon A convergence criterion for the maximum absolute difference of updated values

compared to the previous values. The iteration is completed when all differences

are smaller thanepsilon.

Details

The function iterate.mjca computes the updated Burt matrix. This function is called from the

functionmjcawhen the option lambda="JCA", i.e. when a Joint Correspondence Analysis is per-

formed.

Value

B.star The updated Burt matrix

crit Vector of length 2 containing the number of iterations and epsilon

See Also

mjca


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6 mjca

mjca Multiple and joint correspondence analysis

Description

Computation of multiple and joint correspondence analysis.

Usage

mjca(obj, nd = 2, lambda = c("adjusted", "indicator", "Burt", "JCA"),

supcol = NA, subsetcol = NA,

ps = ":", maxit = 50, epsilon = 0.0001)

Arguments

obj A response pattern matrix (data frame containing factors), or a frequency table(a table object)

nd Number of dimensions to be included in the output; if NA the maximum possible

dimensions are included.

lambda Gives the scaling method. Possible values include "indicator","Burt","adjusted"

and "JCA". Usinglambda = "JCA"results in a joint correspondence analysis

using iterative adjusment of the Burt matrix in the solution space.

supcol Indices of supplementary columns.

subsetcol Indices of subset categories.

ps Separator used for combining variable and category names.

maxit The maximum number of iterations (Joint Correspondence Analysis).

epsilon A convergence criterion (Joint Correspondence Analysis).

Details

The function mjcacomputes a multiple or joint correspondence analysis based on the eigenvalue

decomposition of the Burt matrix.

Value

sv Eigenvalues (lambda = "indicator") or singular values (lambda = "Burt",

"adjusted"or "JCA")

lambda Scaling method

inertia.e Percentages of explained inertia

inertia.t Total inertia

inertia.et Total percentage of explained inertia with thend-dimensional solution

levelnames Names of the factor/level combinations

levels.n Number of levels in each factor


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mjca 7

nd User-specified dimensionality of the solution

nd.max Maximum possible dimensionality of the solution

rownames Row names

rowmass Row massesrowdist Row chi-square distances to centroid

rowinertia Row inertias

rowcoord Row standard coordinates

rowpcoord Row principal coordinates

rowctr Row contributions

rowcor Row squared correlations

colnames Column names

colmass Column masses

coldist Column chi-square distances to centroid

colinertia Column inertias

colcoord Column standard coordinates

colpcoord Column principal coordinates

colctr column contributions

colcor Column squared correlations

colsup Indices of column supplementary points (of the Burt and Indicator matrix)

subsetcol Indices of subset columns

Burt Burt matrix

Burt.upd The updated Burt matrix (JCA only)

subinertia Inertias of sub-matrices

JCA.iter Vector of length two containing the number of iterations and the epsilon (JCA

only)

call Return ofmatch.call

References

Nenadic, O. and Greenacre, M. (2007), Correspondence analysis in R, with two- and three-dimensional

graphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/

v20/i03/

Nenadic, O. and Greenacre, M. (2007), Computation of Multiple Correspondence Analysis, with

Code in R, in Multiple Correspondence Analysis and Related Methods(eds. M. Greenacre and J.

Blasius), Boca Raton: Chapmann & Hall / CRC, pp. 523-551.

Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationshipsamong a selected set of response categories from a questionnaire survey. Sociological Methods and

Research,35, pp. 193-218.

See Also

eigen,plot.mjca,summary.mjca,print.mjca
http://www.jstatsoft.org/v20/i03/http://www.jstatsoft.org/v20/i03/http://www.jstatsoft.org/v20/i03/http://www.jstatsoft.org/v20/i03/


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8 pchlist

Examples

data("wg93")

mjca(wg93[,1:4])

### Different approaches to multiple correspondence analysis:

# Multiple correspondence analysis based on the indicator matrix:

mjca(wg93[,1:4], lambda = "indicator")

# Multiple correspondence analysis based on the Burt matrix:

mjca(wg93[,1:4], lambda = "Burt")

# "Adjusted" multiple correspondence analysis (default setting):

mjca(wg93[,1:4], lambda = "adjusted")

# Joint correspondence analysis:

mjca(wg93[,1:4], lambda = "JCA")

### Subset analysis and supplementary variables:

# Subset analysis:

mjca(wg93[,1:4], subsetcol = (1:20)[-seq(3,18,5)])

# Supplementary variables:

mjca(wg93, supcol = 5:7)

# Combining supplementary variables and a subset analysis:

mjca(wg93, supcol = 5:7, subsetcol = (1:20)[-seq(3,18,5)])

# table input

data(UCBAdmissions)

mjca(UCBAdmissions)

plot(mjca(UCBAdmissions))

pchlist Listing the set of available symbols.

Description

A plot of the available symbols for use with the option pch.

Usage

pchlist()

Details

This function generates a numbered list of the plotting symbols available for use in the functions

plot.caand plot3d.ca.


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plot.ca 9

See Also

plot.ca,plot3d.ca

Examplespchlist()

plot.ca Plotting 2D maps in correspondence analysis

Description

Graphical display of correspondence analysis results in two dimensions

Usage

## S3 method for class ca

plot(x, dim = c(1,2), map = "symmetric", what = c("all", "all"),

mass = c(FALSE, FALSE), contrib = c("none", "none"),

col = c("blue", "red"), pch = c(16, 21, 17, 24),

labels = c(2, 2), arrows = c(FALSE, FALSE),

lines = c(FALSE, FALSE), xlab = "_auto_", ylab = "_auto_",

col.lab = c("blue", "red"), ...)

Arguments

x Simple correspondence analysis object returned byca

dim Numerical vector of length 2 indicating the dimensions to plot on horizontal

and vertical axes respectively; default is first dimension horizontal and seconddimension vertical.

map Character string specifying the map type. Allowed options include

"symmetric"(default)

"rowprincipal"

"colprincipal"

"symbiplot"

"rowgab"

"colgab"

"rowgreen"

"colgreen"

what Vector of two character strings specifying the contents of the plot. First entry

sets the rows and the second entry the columns. Allowed values are

"all"(all available points, default)

"active"(only active points are displayed)

"passive"(only supplementary points are displayed)

"none"(no points are displayed)

The status (active or supplementary) of rows and columns is set in ca using the

optionssuprowand supcol.


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10 plot.ca

mass Vector of two logicals specifying if the mass should be represented by the area

of the point symbols (first entry for rows, second one for columns)

contrib Vector of two character strings specifying if contributions (relative or absolute)

should be represented by different colour intensities. Available options are

"none"(contributions are not indicated in the plot).

"absolute"(absolute contributions are indicated by colour intensities).

"relative"(relative contributions are indicated by colour intensities).

If set to"absolute"or"relative", points with zero contribution are displayed

in white. The higher the contribution of a point, the closer the corresponding

colour to the one specified by the coloption.

col Vector of length 2 specifying the colours of row and column point symbols, by

default blue for rows and red for columns. Colours can be entered in hexadeci-

mal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) values or by R-name (e.g. "red").

pch Vector of length 4 giving the type of points to be used for row active and sup-

plementary, column active and supplementary points. Seepchlistfor a list of

symbols.

labels Vector of length two specifying if the plot should contain symbols only (0),

labels only (1) or both symbols and labels (2). Settinglabelsto 2results in the

symbols being plotted at the coordinates and the labels with an offset.

arrows Vector of two logicals specifying if the plot should contain points (FALSE, de-

fault) or arrows (TRUE). First value sets the rows and the second value sets the

columns.

lines Vector of two logicals specifying if the plot should join the points with lines

(FALSE, default) or arrows (TRUE). First value sets the rows and the second value

sets the columns.

xlab, ylab Labels for horizontal and vertical axes. The default,"_auto_"means that the

function auto-generates a label of the form Dimension X (xx.xx %

col.lab Vector of length 2 specifying the colours of row and column point labels

... Further arguments passed toplotand points.

Details

The functionplot.camakes a two-dimensional map of the object created by cawith respect to two

selected dimensions. By default the scaling option of the map is "symmetric", that is the so-called

symmetric map. In this map both the row and column points are scaled to have inertias (weighted

variances) equal to the principal inertia (eigenvalue or squared singular value) along the principal

axes, that is both rows and columns are in pricipal coordinates. Other options are as follows:

-"rowprincipal"or "colprincipal"- these are the so-called asymmetric maps, with either

rows in principal coordinates and columns in standard coordinates, or vice versa (also known

as row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

-"symbiplot"- this scales both rows and columns to have variances equal to the singular

values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve

row or column metrics;


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plot.ca 11

-"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively,

columns) in principal coordinates and columns (respectively, rows) in standard coordinates

multiplied by the mass of the corresponding point. These are also biplots and were proposed

by Gabriel & Odoroff (1990);

-"rowgreen"or "colgreen" - these are similar to "rowgab" and "colgab" except that the

points in standard coordinates are multiplied by the square root of the corresponding masses,

giving reconstructions of the standardized residuals.

This function has options for sizing and shading the points. If the option massis TRUEfor a set of

points, the size of the point symbol is proportional to the relative frequency (mass) of each point.

If the option contrib is "absolute" or "relative" for a set of points, the colour intensity of

the point symbol is proportional to the absolute contribution of the points to the planar display or,

respectively, the quality of representation of the points in the display. To globally resize all the

points (and text labels), use par("cex"=)before the plot.

Value

In addition to the side effect of producing the plot, the function invisibly returns the coordinates

of the plotted points, a list of two components, with names rowsand cols. These can be used to

further annotate the plot using base R plotting functions.

References

Gabriel, K.R. and Odoroff, C. (1990). Biplots in biomedical research. Statistics in Medicine,9, pp.

469-485.

Greenacre, M.J. (1993)Correspondence Analysis in Practice. London: Academic Press.

Greenacre, M.J. (1993) Biplots in correspondence Analysis, Journal of Applied Statistics, 20, pp.

251 - 269.

See Alsoca,summary.ca,print.ca,plot3d.ca,pchlist

Examples

data("smoke")

# A two-dimensional map with standard settings

plot(ca(smoke))

# Mass for rows and columns represented by the size of the point symbols

plot(ca(smoke), mass = c(TRUE, TRUE))

# Displaying the column profiles only with masses represented by size of point

# symbols and relative contributions by colour intensity.

# Since the arguments are recycled it is sufficient to give only one argument

# for mass and contrib.

data("author")

plot(ca(author), what = c("none", "all"), mass = TRUE, contrib = "relative")


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12 plot.mjca

plot.mjca Plotting 2D maps in multiple and joint correspondence analysis

Description

Graphical display of multiple and joint correspondence analysis results in two dimensions

Usage

## S3 method for class mjca

plot(x, dim = c(1,2), map = "symmetric", centroids = FALSE,

what = c("none", "all"), mass = c(FALSE, FALSE),

contrib = c("none", "none"), col = c("#000000", "#FF0000"),

pch = c(16, 1, 17, 24), labels = c(2, 2),

arrows = c(FALSE, FALSE), xlab = "_auto_", ylab = "_auto_", ...)

Arguments

x Multiple or joint correspondence analysis object returned bymjca

dim Numerical vector of length 2 indicating the dimensions to plot on horizontal

and vertical axes respectively; default is first dimension horizontal and second

dimension vertical.

map Character string specifying the map type. Allowed options include

"symmetric"(default)

"rowprincipal"

"colprincipal"

"symbiplot"

"rowgab""colgab"

"rowgreen"

"colgreen"

centroids Logical indicating if column centroids should be added to the plot



"all"(all available points, default)

"active"(only active points are displayed)

"passive"(only supplementary points are displayed)


The status (active or supplementary) of columns is set in mjcausing the option

supcol.mass Vector of two logicals specifying if the mass should be represented by the area

of the point symbols (first entry for rows, second one for columns)


should be represented by different colour intensities. Available options are



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plot.mjca 13


"relative"(relative contributions are indicated by colour intensities).




col Vector of length 2 specifying the colours of row and column point symbols, by

default black for rows and red for columns. Colours can be entered in hexadeci-

mal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) values or by R-name (e.g. "red").

pch Vector of length 4 giving the type of points to be used for row active and sup-

plementary, column active and supplementary points. Seepchlistfor a list of

symbols.





fault) or arrows (TRUE

). First value sets the rows and the second value sets thecolumns.

xlab, ylab Labels for horizontal and vertical axes. The default,"_auto_"means that the

function auto-generates a label of the form Dimension X (xx.xx %

... Further arguments passed toplotand points.

Details

The functionplot.mjcamakes a two-dimensional map of the object created by mjcawith respect

to two selected dimensions. By default the scaling option of the map is "symmetric", that is the

so-calledsymmetric map. In this map both the row and column points are scaled to have inertias

(weighted variances) equal to the principal inertia (eigenvalue) along the principal axes, that is both

rows and columns are in pricipal coordinates. Other options are as follows:

-"rowprincipal"or "colprincipal"- these are the so-called asymmetric maps, with either

rows in principal coordinates and columns in standard coordinates, or vice versa (also known

as row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

-"symbiplot"- this scales both rows and columns to have variances equal to the singular

values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve

row or column metrics;

-"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively,

columns) in principal coordinates and columns (respectively, rows) in standard coordinates

multiplied by the mass of the corresponding point. These are also biplots and were proposed

by Gabriel & Odoroff (1990);

-"rowgreen"or "colgreen" - these are similar to "rowgab" and "colgab" except that the

points in standard coordinates are multiplied by the square root of the corresponding masses,

giving reconstructions of the standardized residuals.

This function has options for sizing and shading the points. If the option massis TRUEfor a set of

points, the size of the point symbol is proportional to the relative frequency (mass) of each point.


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14 plot3d.ca

If the option contrib is "absolute" or "relative" for a set of points, the colour intensity of

the point symbol is proportional to the absolute contribution of the points to the planar display or,

respectively, the quality of representation of the points in the display. To globally resize all the

points (and text labels), use par("cex"=)before the plot.

Value

In addition to the side effect of producing the plot, the function invisibly returns the coordinates

of the plotted points, a list of two components, with names rowsand cols. These can be used to

further annotate the plot using base R plotting functions.

References

Gabriel, K.R. and Odoroff, C. (1990). Biplots in biomedical research. Statistics in Medicine,9, pp.

469-485.

Greenacre, M.J. (1993)Correspondence Analysis in Practice. London: Academic Press.

Greenacre, M.J. (1993) Biplots in correspondence Analysis, Journal of Applied Statistics, 20, pp.

251 - 269.

See Also

mjca,summary.mjca,print.mjca,pchlist

Examples

data("wg93")

# A two-dimensional map with standard settings

plot(mjca(wg93[,1:4]))

plot3d.ca Plotting 3D maps in correspondence analysis

Description

Graphical display of correspondence analysis in three dimensions

Usage


plot3d(x, dim = c(1, 2, 3), map = "symmetric", what = c("all", "all"),

contrib = c("none", "none"), col = c("#6666FF","#FF6666"),

labcol = c("#0000FF", "#FF0000"), pch = c(16, 1, 18, 9),

labels = c(2, 2), sf = 0.00002, arrows = c(FALSE, FALSE), ...)


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plot3d.ca 15

Arguments

x Simple correspondence analysis object returned by ca

dim Numerical vector of length 2 indicating the dimensions to plot

map Character string specifying the map type. Allowed options include"symmetric"(default)

"rowprincipal"

"colprincipal"

"symbiplot"

"rowgab"

"colgab"

"rowgreen"

"colgreen"




"active"(only active points are displayed, default)"supplementary"(only supplementary points are displayed)

"all"(all available points)

The status (active or supplementary) is set in ca.


should be indicated by different colour intensities. Available options are



"relative"(relative conrributions are indicated by colour intensities).




col Vector of length 2 specifying the colours of row and column profiles. Colourscan be entered in hexadecimal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) values

or by R-name (e.g. "red").

labcol Vector of length 2 specifying the colours of row and column labels.

pch Vector of length 2 giving the type of points to be used for rows and columns.




sf A scaling factor for the volume of the 3d primitives.


fault) or arrows (TRUE). First value sets the rows and the second value sets the

columns.

... Further arguments passed to the rgl functions.

See Also

ca


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16 print.mjca

print.ca Printing ca objects

Description

Printing method for correspondence analysis objects

Usage


print(x, ...)

Arguments

x Simple correspondence analysis object returned byca

... Further arguments are ignored

Details

The functionprint.cagives the basic statistics of the caobject. First the eigenvalues (that is, prin-

cipal inertias) and their percentages with respect to total inertia are printed. Then for the rows and

columns respectively, the following are printed: the masses, chi-square distances of the points to the

centroid (i.e., centroid of the active points), point inertias (for active points only) and principal co-

ordinates on the firstnd dimensions requested (default = 2 dimensions). The function summary.ca

gives more detailed results about the inertia contributions of each point on each principal axis.

For supplementary points, masses and inertias are not applicable.

See Also

ca

Examples

data("smoke")

print(ca(smoke))

print.mjca Printing mjca objects

Description

Printing method for multiple and joint correspondence analysis objects

Usage


print(x, ...)


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print.summary.ca 17

Arguments

x Multiple or joint correspondence analysis object returned bymjca


Details

The function print.mjcagives the basic statistics of the mjca object. First the eigenvalues (that

is, principal inertias) and their percentages with respect to total inertia are printed. Then for the

rows and columns respectively, the following are printed: the masses, chi-square distances of the

points to the centroid (i.e., centroid of the active points), point inertias (for active points only) and

principal coordinates on the first nd dimensions requested (default = 2 dimensions). The function

summary.mjcagives more detailed results about the inertia contributions of each point on each

principal axis.

For supplementary points, masses and inertias are not applicable.

See Also

mjca

Examples

data("wg93")

print(mjca(wg93[,1:4]))

# equivalent to:

mjca(wg93[,1:4])

print.summary.ca Printing summeries of ca objects

Description

Printing method for summaries of correspondence analysis objects

Usage

## S3 method for class summary.ca

print(x, ...)

Arguments

x Summary of a simple correspondence analysis object returned bysummary.ca


See Also

ca,summary.ca


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18 smoke

print.summary.mjca Printing summeries of mjca objects

Description

Printing method for summaries of multiple and joint correspondence analysis objects

Usage

## S3 method for class summary.mjca

print(x, ...)

Arguments

x summary of a multiple or joint correspondence analysis object returned by summary.mjca


See Also

mjca,summary.mjca

smoke Smoke dataset

Description

Artificial dataset in Greenacre (1984)

Usage

data(smoke)

Format

Table containing 5 rows (staff group) and 4 columns (smoking categories), giving the frequencies

of smoking categories in each staff group in a fictional organization.

References

Greenacre, M.J. (1984). Theory and Applications of Correspondence Analysis. London: Academic

Press.


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summary.ca 19

summary.ca Summarizing simple correspondence analysis

Description

Textual output summarizing the results ofca, including a scree-plot of the principal inertias and

row and column contributions.

Usage


summary(object, scree = TRUE, ...)

Arguments

object Simple correspondence analysis object returned byca.

scree Logical flag specifying if a scree-plot should be included in the output.

... Further arguments (ignored)

Details

The function summary.ca gives the detailed numerical results of the ca function. All the eigenvalues

(principal inertias) are listed, their percentages with respect to total inertia, and a bar chart (alsoknown as a scree plot). Then for the set of rows and columns a table of results is given in a standard

format, where quantities are either multiplied by 1000 or expressed in permills (thousandths): the

mass of each point (x1000), the quality of display in the solution subspace ofnd dimensions, the

inertia of the point (in permills of the total inertia), and then for each dimension of the solution

the principal coordinate (x1000), the (relative) contribution COR of the principal axis to the point

inertia (x1000) and the (absolute) contribution CTR of the point to the inertia of the axis (in permills

of the principal inertia).

For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, but

the relative contributions (COR) are valid as well as their sum over the set of chosen nddimensions

(QLT).

Examples

data("smoke")

summary(ca(smoke))


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20 summary.mjca

summary.mjca Summarizing multiple and joint correspondence analysis

Description

Textual output summarizing the results ofmjca,including a scree-plot of the principal inertias and

row and column contributions.

Usage


summary(object, scree = TRUE, rows = FALSE, ...)

Arguments

object Multiple or joint correspondence analysis object returned bymjca.

scree Logical flag specifying if a scree-plot should be included in the output.

rows Logical specifing whether the results for the rows should be included in the

output (default =FALSE).

... Further arguments (ignored)

Details

The functionsummary.mjca

gives the detailed numerical results of the mjca

function. All theeigenvalues (principal inertias) are listed, their percentages with respect to total inertia, and a bar

chart (also known as a scree plot). Then for the set of rows and columns a table of results is

given in a standard format, where quantities are either multiplied by 1000 or expressed in permills

(thousandths): the mass of each point (x1000), the quality of display in the solution subspace ofnd

dimensions, the inertia of the point (in permills of the total inertia), and then for each dimension of

the solution the principal coordinate (x1000), the (relative) contribution COR of the principal axis

to the point inertia (x1000) and the (absolute) contribution CTR of the point to the inertia of the

axis (in permills of the principal inertia).

For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, but

the relative contributions (COR) are valid as well as their sum over the set of chosen nddimensions

(QLT).

Examples

data("wg93")

summary(mjca(wg93[,1:4]))


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wg93 21

wg93 International Social Survey Program on Environment 1993 - western

German sample

Description

This data frame contains records of four questions on attitude towards science with responses on

a five-point scale (1=agree strongly to 5=disagree strongly) and three demographic variables (sex,

age and education).

Usage

data(wg93)

Format

Data frame (871x7).

Source

ISSP (1993). International Social Survey Program: Environment. http://www.issp.org
http://www.issp.org/http://www.issp.org/


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Index

Topicdatasetsauthor,2

smoke,18

wg93,21

Topicmultivariateca,2

iterate.mjca,5

mjca,6

author,2

ca,2,9,11,1517,19

eigen,7

iterate.mjca,5

mjca,5,6,12,14,17,18,20

pchlist,8,10,11,13,14

plot,10,13

plot.ca,4,8,9,9

plot.mjca,7,12

plot3d.ca,4,8,9,11,14

points,10,13

print.ca,4,11,16

print.mjca,7,14,16

print.summary.ca,17

print.summary.mjca,18

smoke,18

summary.ca,4,11,16,17,19

summary.mjca,7,14,17,18,20

svd,4

wg93,21

22

CA Package

Documents

Transcript of CA Package